Graph coloring is a well known problem from graph theory that, when solving it with local search algorithms, is typically treated as a series of constraint satisfaction problems: for a given number of colors k, one has to find a feasible coloring; once such a coloring is found, the number of colors is decreased and the local search starts again. Here we explore the application of Iterated Local...

Graph coloring is a well known problem from graph theory that, when attacking it with local search algorithms, is typically treated as a series of constraint satisfaction problems: for a given number of colors one has to find a feasible coloring; once such a coloring is found, the number of colors is decreased and the local search starts again. Here we explore the application of Iterated Local ...

In the precoloring extension problem (PrExt) a graph is given with some of the vertices having a preassigned color and it has to be decided whether this coloring can be extended to a proper coloring of the graph with the given number of colors. Two parameterized versions of the problem are studied in the paper: either the number of precolored vertices or the number of colors used in the precolo...

Combinatorial optimization is a fundamental problem found in many fields. In many real life situations, the constraints and the objective function forming the optimization problem are naturally distributed amongst different sites in some fashion. A typical approach for solving such problem is to collect all of this information together and centrally solve the problem. However, this requires all...

The graph coloring problem is often investigated in the literature. Many insights about many neighboring solutions with the same fitness value are raised but as far as we know, no deep analysis of this neutrality has ever been conducted in the literature. In this paper, we quantify the neutrality of some hard instances of the graph coloring problem. This neutrality property has to be detected a...

In this paper a new parallel genetic algorithm for coloring graph vertices is presented. In the algorithm we apply a migration model of parallelism and de ne two new recombination operators: SPPX and CEX. For comparison two recently proposed crossover operators: UISX and GPX are selected. The performance of the algorithm is veri ed by computer experiments on a set of standard graph coloring ins...

---------------------------------------------------------------------***--------------------------------------------------------------------Abstract— In this paper we have proposed a new Particle Swarm Optimization algorithm named Enhanced PSO. The proposed strategy consists of the concept of the Smallest Position Value rule. In this case the solution having the smallest position value will be ...

In this paper we propose a deterministic parallel graph coloring algorithm that enables Multi-Coloring in parallel for sparse undirected graphs by coarse-grained segmentation and symmetry breaking. The proposed algorithm is implemented and tested on standard problem instances from engineering applications and benchmarked against various deterministic graph coloring algorithms. Quantified result...

This lecture deals with the problem of proper vertex colorings of graphs. More speciically, we are interested in coloring a given 3-colorable graph with as few colors as we can. It is easy to see that it is NP-Hard to nd a 3 coloring for any given 3-colorable graph-this would enable deciding whether a general graph is 3-colorable. If a polynomial-time algorithm existed for 3-coloring a 3-colora...

A graph is k-choosable if it admits a proper coloring of its vertices for every assignment of k (possibly different) allowed colors to choose from for each vertex. It is NP-hard to decide whether a given graph is k-choosable for k ≥ 3, and this problem is considered strictly harder than the k-coloring problem. Only few positive results are known on input graphs with a given structure. Here, we ...